Your teacher is giving you a test worth of 100 points containing 40 questions. There are two point and four point questions on the test. How many of each type of questions are on the test?

1 Answer
MeneerNask
Nov 14, 2016

If all the questions were 2-pt questions there would be 80 points total, which is 20 pt short.

Explanation:

Every 2-pt replaced by a 4-pt will add 2 to the total.
You'll have to do this #20div2=10# times.

Answer: #10# 4-pt questions and #40-10=30# 2-pt questions.

The algebraic approach:
We call the number of 4-pt qustions #=x#
Then the number of 2-pt questions #=40-x#

Total points: #=4*x+2*(40-x)=100#
Working away the brackets:
#4x+80-2x=100#

Subtract 80 on both sides:
#4x+cancel80-cancel80-2x=100-80#

#->2x=20->x=10# 4-pt questions
#->40-x=40-10=30# 2-pt questions.

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